Question

Fill in the missing statement and reason of the proof below.

Given: A, B, C, DABCD is a rhombus.

Prove: start overline, D, E, end overline, \cong, start overline, B, E, end overline
DE
≅
BE
.
In the proof shown in the table below, one of the steps in the middle is missing. Before completing the missing step, make sure to read the steps that come after it. To complete the missing step, first use the dropdown menu in the statement column to select the format of the statement for that step. Once you select a format, a statement will appear with input boxes and/or dropdowns to complete, and a dropdown menu will appear in the reason column. Once completed, press the submit button in the answer area at the bottom of the page. The diagram associated with this problem is located below the proof table, and is available as a tactile printout. There may be a clarifying note below the diagram.
Step Statement Reason
1
A, B, C, DABCD is a rhombus
Given
2
start overline, A, C, end overline
AC
bisects angle, D, C, B∠DCB
The diagonals of a rhombus bisect the interior angles
3
angle, D, C, A, \cong, angle, B, C, A∠DCA≅∠BCA
An angle bisector divides an angle into two congruent angles
4
angle, D, C, A∠DCA and angle, D, C, E∠DCE are supplementary
If two angles form a linear pair, then they are supplementary
5
angle, B, C, A∠BCA and angle, B, C, E∠BCE are supplementary
If two angles form a linear pair, then they are supplementary
6
angle, D, C, E, \cong, angle, B, C, E∠DCE≅∠BCE
If two angles are supplements of the same angle (or congruent angles), then they are congruent
7
start overline, C, E, end overline, \cong, start overline, C, E, end overline
CE
≅
CE

Reflexive Property
8
start overline, D, C, end overline, \cong, start overline, B, C, end overline
DC
≅
BC

All sides of a rhombus are congruent
9 type of statement
10
start overline, D, E, end overline, \cong, start overline, B, E, end overline
DE
≅
BE

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

Answer 1

Step 9 statement: ΔDCE ≅ ΔBCE

Reason: SAS (Side-Angle-Side) Congruence Postulate (DC ≅ BC, ∠DCE ≅ ∠BCE, CE ≅ CE)